Bootstrap for Testing the Existence of Finite Moments : A Caution for Possible Misapplication

This paper discusses a bootstrap-based test that checks if finite moments exist and indicates cases of possible misapplication. It notes, in fact, that a procedure for finding the smallest power to which a sample needs to be raised, such that the test rejects a hypothesis that the corresponding moment is finite works poorly as an estimator of the tail index or moment estimator. Several examples of correct usage of the test are also shown. The main result is derived analytically, and a numerical Monte-Carlo example is presented